On the Critical Kirchhoff Problems with Super-linear Nonlinearities and Variable Potentials

作者：Xiao, Ting; Zhang, Qiongfen^*

来源：Bulletin of the Iranian Mathematical Society, 2022, 48(6): 3351-3380.

DOI：10.1007/s41980-022-00699-8

• Kirchhoff-type equation
• Ground state solution
• Critical growth

In this paper, we consider the following critical Kirchhoff equation: @@@ -(a + b integral(R3) vertical bar del u vertical bar(2)dx) Delta u + V(x)u = mu f(u) +u(5), x is an element of R-3, @@@ where mu is a positive parameter, a, b > 0 are real constants, f is an element of C(R, R) and V is an element of C-1 (R-3, R). Under some suitable conditions, the existence of ground state solution to the above problem is established without the monotonicity condition on f (u)/u(3) Moreover, it is worth noting that we consider the above problem with variable potentials. Our results improve and extend related ones in the existing literature to some extent.

• 单位
  桂林理工大学